Now I own neither of these calibers, but if I am going to shoot a moose or an elk I rather have a 7 mm Mag.

I have both. The .308 Win is cheaper to shoot, and is an excellent deer cartridge that with proper shot placement is also good for elk. I have only killed one pronghorn antelope with mine.

The 7 mm Rem mag will have more velocity and energy at all ranges than a .308 Win, and is an excellent cartridge for all animals up to and including elk and moose. I have used my 7 mm RM for deer, pronghorn antelope, elk, caribou, musk ox, and a variety of African animals up to Kudu.